Constitutive modelling of granular materials using a contact normal-based fabric tensor

Abstract

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress-strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

Quantitative Description for Sand Void Fabric with the Principle of Stereology

“…where M i 1 i 2 ...i n is the void fabric tensor, which is used for the microscopic quantitative detection of the void tensor directly. The tensor determined by Equation (7) accurately describes the variation of void space distribution in theory. However, in practice, the second-order fabric tensor has been able to describe the variation of void distribution.…”

“…Hence, the influence of higher-order tensors is ignored. Equation (7) describes the second-order tensor as follows.…”

“…Sun et al [5] and Zheng et al [6] found that the void fabric tensor and particle sphericity, relative density, and coordination number have a strong functional relationship through the image analysis of loose and dense sand specimens. Hu et al [7] presented a fabric tensor-based bounding surface model accounting for the anisotropic behavior of granular materials. Zhang et al [8] established the relations between the macroscopic volumetric strain, shear strain, and void fabric combined with the micromechanics theory, and linked with void fabric tensor.…”

On the evolution law of a contact normal-based fabric tensor for granular materials

“…induced anisotropy). Fabric anisotropy and its evolution may exert significant effects on the strength and deformation properties of discrete granular materials [1,4,17,[22][23][24], for example, the shear strength [20,[25][26][27], elastic moduli [28], non-coaxial plastic flow [29][30][31][32] and dilatancy [10,[33][34][35]. These behaviours of granular materials are closely associated with the stability and buckling of force chains at a mesoscopic scale and sliding and rolling at contacts, thus governed by the grain-scale structural characteristics and processes.…”

Three‐dimensional anisotropic plasticity model for sand subjected to principal stress value change and axes rotation

“…Overcoming these limitations requires understanding of the dilatancy, 12,13,17,20,23 hardening, 12,17,20 noncoaxiality between strain rate and stress, 12,20,24 and fabric evolution and its effects 21,25–31 under PSAR , which can be enhanced not only by laboratory tests, 32–37 but also by discrete element method (DEM) 38 numerical tests, which allow for more control over stress path and easier microscopic observations 7,8,39,40 …”